Transcript Preprocess

浙江大学本科生《数据挖掘导论》课件
第2课 数据预处理技术
徐从富，副教授
浙江大学人工智能研究所
内容提纲

Why preprocess the data?

Data cleaning

Data integration and transformation

Data reduction

Discretization and concept hierarchy
generation

Summary
I.

Why Data Preprocessing?
Data in the real world is dirty
 incomplete:
lacking attribute values, lacking certain
attributes of interest, or containing only aggregate data

e.g., occupation=“”
 noisy:

containing errors or outliers
e.g., Salary=“-10”
 inconsistent:



containing discrepancies in codes or names
e.g., Age=“42” Birthday=“03/07/1997”
e.g., Was rating “1,2,3”, now rating “A, B, C”
e.g., discrepancy between duplicate records
Why Is Data Dirty?



Incomplete data comes from

n/a data value when collected

different consideration between the time when the data was collected
and when it is analyzed.

human/hardware/software problems
Noisy data comes from the process of data

collection

entry

transmission
Inconsistent data comes from

Different data sources

Functional dependency violation
Why Is Data Preprocessing Important?

No quality data, no quality mining results!
 Quality

decisions must be based on quality data
e.g., duplicate or missing data may cause incorrect or
even misleading statistics.
 Data
warehouse needs consistent integration of
quality data

Data extraction, cleaning, and transformation
comprises the majority of the work of building a
data warehouse. —Bill Inmon
Multi-Dimensional Measure of Data
Quality

A well-accepted multidimensional view:
 Accuracy
 Completeness
 Consistency
 Timeliness
 Believability
 Value
added
 Interpretability
 Accessibility

Broad categories:
 intrinsic, contextual, representational, and
accessibility.
Major Tasks in Data Preprocessing

Data cleaning


Data integration


Normalization and aggregation
Data reduction


Integration of multiple databases, data cubes, or files
Data transformation


Fill in missing values, smooth noisy data, identify or remove outliers,
and resolve inconsistencies
Obtains reduced representation in volume but produces the same or
similar analytical results
Data discretization

Part of data reduction but with particular importance, especially for
numerical data
Forms of data preprocessing
II.

Data Cleaning
Importance
 “Data
cleaning is one of the three biggest problems in
data warehousing”—Ralph Kimball
 “Data cleaning is the number one problem in data
warehousing”—DCI survey

Data cleaning tasks
 Fill
in missing values
 Identify outliers and smooth out noisy data
 Correct inconsistent data
 Resolve redundancy caused by data integration
Missing Data

Data is not always available



E.g., many tuples have no recorded value for several attributes, such
as customer income in sales data
Missing data may be due to

equipment malfunction

inconsistent with other recorded data and thus deleted

data not entered due to misunderstanding

certain data may not be considered important at the time of entry

not register history or changes of the data
Missing data may need to be inferred.
How to Handle Missing Data?

Ignore the tuple
usually done when class label is missing (assuming the tasks in
classification—not effective when the percentage of missing
values per attribute varies considerably).

Fill in the missing value manually
tedious + infeasible?

Fill in it automatically with




a global constant : e.g., “unknown”, a new class?!
the attribute mean
the attribute mean for all samples belonging to the same class: smarter
the most probable value: inference-based such as Bayesian formula or
decision tree
Noisy Data


Noise: random error or variance in a measured
variable
Incorrect attribute values may due to
 faulty data collection instruments
 data entry problems
 data transmission problems
 technology limitation
 inconsistency in naming convention

Other data problems which requires data cleaning
 duplicate records
 incomplete data
 inconsistent data
How to Handle Noisy Data?

Binning method:
 first
sort data and partition into (equi-depth) bins
 then one can smooth by bin means, smooth by bin median,
smooth by bin boundaries, etc.

Clustering
 detect and

remove outliers
Combined computer and human inspection
 detect suspicious
values and check by human (e.g., deal
with possible outliers)

Regression
 smooth
by fitting the data into regression functions
Simple Discretization Methods: Binning

Equal-width (distance) partitioning:
 Divides
the range into N intervals of equal size: uniform
grid
 if A and B are the lowest and highest values of the
attribute, the width of intervals will be: W = (B –A)/N.
 The most straightforward, but outliers may dominate
presentation
 Skewed data is not handled well.

Equal-depth (frequency) partitioning:
 Divides
the range into N intervals, each containing
approximately same number of samples
 Good data scaling
 Managing categorical attributes can be tricky.
Binning Methods for Data Smoothing
•
Sorted data for price (in dollars)
4, 8, 9, 15, 21, 21, 24, 25, 26, 28, 29, 34
* Partition into (equi-depth) bins:
- Bin 1: 4, 8, 9, 15
- Bin 2: 21, 21, 24, 25
- Bin 3: 26, 28, 29, 34
* Smoothing by bin means:
- Bin 1: 9, 9, 9, 9
- Bin 2: 23, 23, 23, 23
- Bin 3: 29, 29, 29, 29
* Smoothing by bin boundaries:
- Bin 1: 4, 4, 4, 15
- Bin 2: 21, 21, 25, 25
- Bin 3: 26, 26, 26, 34
Cluster Analysis
Regression
y
Y1
Y1’
y=x+1
X1
x
III. Data Integration

Data integration:
 combines

data from multiple sources into a coherent store
Schema integration
 integrate metadata
from different sources
 Entity identification problem: identify real world entities from
multiple data sources, e.g., A.cust-id  B.cust-#

Detecting and resolving data value conflicts
 for
the same real world entity, attribute values from different
sources are different
 possible reasons: different representations, different scales,
e.g., metric vs. British units
Handling Redundancy in Data Integration

Redundant data occur often when integration of multiple
databases
 The
same attribute may have different names in different
databases
 One
attribute may be a “derived” attribute in another table,
e.g., annual revenue

Redundant data may be able to be detected by cor-relational
analysis

Careful integration of the data from multiple sources may help
reduce/avoid redundancies and inconsistencies and improve
mining speed and quality
Data Transformation

Smoothing: remove noise from data

Aggregation: summarization, data cube construction

Generalization: concept hierarchy climbing

Normalization: scaled to fall within a small,
specified range
 min-max normalization
 z-score normalization
 normalization by decimal

scaling
Attribute/feature construction
 New
attributes constructed from the given ones
Data Transformation: Normalization

min-max normalization（最小-最大规范化）
v  minA
v' 
(new _ maxA  new _ minA)  new _ minA
maxA  minA

z-score normalization（z-score规范化）
v  meanA
v' 
stand_devA

normalization by decimal scaling（小数定标规范化）
v
v'  j
10
Where j is the smallest integer such that Max(| v ' |)<1
IV. Data Reduction Strategies



A data warehouse may store terabytes of data
 Complex data analysis/mining may take a very long time to run
on the complete data set
Data reduction
 Obtain a reduced representation of the data set that is much
smaller in volume but yet produce the same (or almost the same)
analytical results
Data reduction strategies
 Data cube aggregation（数据立方体聚集）
 Dimensionality reduction—remove unimportant attributes
 Data Compression
 Numerosity reduction—fit data into models
 Discretization and concept hierarchy generation
Data Cube Aggregation

The lowest level of a data cube
 the
aggregated data for an individual entity of interest
 e.g.,

a customer in a phone calling data warehouse.
Multiple levels of aggregation in data cubes
 Further

reduce the size of data to deal with
Reference appropriate levels
 Use
the smallest representation which is enough to solve the
task

Queries regarding aggregated information should be answered
using data cube, when possible
Dimensionality Reduction

Feature selection (i.e., attribute subset selection):
 Select a
minimum set of features such that the probability
distribution of different classes given the values for those
features is as close as possible to the original distribution
given the values of all features
 reduce # of patterns in the patterns, easier to understand

Heuristic methods (due to exponential # of choices):
 step-wise
forward selection（逐步向前选择）
 step-wise backward elimination（逐步向后删除）
 combining forward selection and backward elimination
 decision-tree induction
Example of Decision Tree Induction
Initial attribute set:
{A1, A2, A3, A4, A5, A6}
A4 ?
A6?
A1?
Class 1
>
Class 2
Class 1
Reduced attribute set: {A1, A4, A6}
Class 2
Data Compression

String compression
 There
are extensive theories and well-tuned algorithms
 Typically lossless
 But only limited manipulation is possible without expansion

Audio/video compression
 Typically lossy
compression, with progressive refinement
 Sometimes small fragments of signal can be reconstructed
without reconstructing the whole

Time sequence is not audio
 Typically short
and vary slowly with time
Data Compression
Compressed
Data
Original Data
lossless
Original Data
Approximated
Wavelet Transformation
Haar2
Daubechie4

Discrete wavelet transform (DWT): linear signal processing,
multiresolutional analysis

Compressed approximation: store only a small fraction of the strongest of the
wavelet coefficients

Similar to discrete Fourier transform (DFT), but better lossy compression,
localized in space

Method:

Length, L, must be an integer power of 2 (padding with 0s, when
necessary)

Each transform has 2 functions: smoothing, difference

Applies to pairs of data, resulting in two set of data of length L/2

Applies two functions recursively, until reaches the desired length
Principal Component Analysis

Given N data vectors from k-dimensions, find c <= k
orthogonal vectors that can be best used to represent
data
 The
original data set is reduced to one consisting of N data
vectors on c principal components (reduced dimensions)

Each data vector is a linear combination of the c
principal component vectors

Works for numeric data only

Used when the number of dimensions is large
Principal Component Analysis
X2
Y1
Y2
X1
Numerosity Reduction（数值归约）

Parametric methods
 Assume
the data fits some model, estimate model
parameters, store only the parameters, and discard the
data (except possible outliers)
 Log-linear models:
obtain value at a point in m-D space
as the product on appropriate marginal subspaces

Non-parametric methods
 Do
not assume models
 Major
families: histograms, clustering, sampling
Regression and Log-Linear Models

Linear regression: Data are modeled to fit a straight line
 Often
uses the least-square method to fit the line

Multiple regression: allows a response variable Y to be
modeled as a linear function of multidimensional feature
vector

Log-linear model: approximates discrete multidimensional
probability distributions
Regress Analysis and Log-Linear Models

Linear regression: Y =  +  X
parameters ,  and  specify the line and are to be
estimated by using the data at hand.
 using the least squares criterion to the known values of Y1,
Y2, …, X1, X2, ….
 Two

Multiple regression: Y = b0 + b1X1 + b2X2.
 Many

nonlinear functions can be transformed into the above.
Log-linear models:
 The
multi-way table of joint probabilities is approximated by
a product of lower-order tables.
 Probability:
p(a, b, c, d) = ab acad bcd
Histograms




A popular data
reduction technique
Divide data into
buckets and store
average (sum) for each
bucket
Can be constructed
optimally in one
dimension using
dynamic programming
Related to quantization
problems.
40
35
30
25
20
15
10
5
0
10000
30000
50000
70000
90000
Clustering




Partition data set into clusters, and one can store
cluster representation only
Can be very effective if data is clustered but not if
data is “smeared”
Can have hierarchical clustering and be stored in
multi-dimensional index tree structures
There are many choices of clustering definitions and
clustering algorithms, further detailed in future
Sampling


Allow a mining algorithm to run in complexity that is
potentially sub-linear to the size of the data
Choose a representative subset of the data
 Simple
random sampling may have very poor performance
in the presence of skew

Develop adaptive sampling methods
 Stratified sampling（分层采样）:
Approximate the percentage of each class (or
subpopulation of interest) in the overall database
 Used in conjunction with skewed data


Sampling may not reduce database I/Os (page at a
time).
Sampling
Raw Data
Sampling
Raw Data
Cluster/Stratified Sample
Hierarchical Reduction




Use multi-resolution structure with different degrees of
reduction
Hierarchical clustering is often performed but tends to define
partitions of data sets rather than “clusters”
Parametric methods are usually not amenable to hierarchical
representation
Hierarchical aggregation
 An index tree hierarchically divides a data set into partitions
by value range of some attributes
 Each partition can be considered as a bucket
 Thus an index tree with aggregates stored at each node is a
hierarchical histogram
V.

Discretization
Three types of attributes:
— values from an unordered set
 Ordinal — values from an ordered set
 Continuous — real numbers
 Nominal

Discretization:
 divide
the range of a continuous attribute into intervals
 Some classification algorithms only accept categorical
attributes.
 Reduce data size by discretization
 Prepare for further analysis
Discretization and Concept hierachy

Discretization
 reduce
the number of values for a given continuous
attribute by dividing the range of the attribute into intervals.
Interval labels can then be used to replace actual data
values

Concept hierarchies
 reduce
the data by collecting and replacing low level
concepts (such as numeric values for the attribute age) by
higher level concepts (such as young, middle-aged, or
senior)
Discretization and Concept Hierarchy
Generation for Numeric Data

Binning (see sections before)

Histogram analysis (see sections before)

Clustering analysis (see sections before)

Entropy-based discretization

Segmentation by natural partitioning
Entropy-Based Discretization

Given a set of samples S, if S is partitioned into two intervals
S1 and S2 using boundary T, the entropy after partitioning is
E (S ,T ) 



| S1|
| S|
Ent ( S1) 
|S 2|
| S|
Ent ( S 2)
The boundary that minimizes the entropy function over all
possible boundaries is selected as a binary discretization.
The process is recursively applied to partitions obtained until
some stopping criterion is met, e.g., Ent ( S )  E (T , S )  
Experiments show that it may reduce data size and improve
classification accuracy
Segmentation by Natural Partitioning

A simply 3-4-5 rule can be used to segment numeric data into
relatively uniform, “natural” intervals.

If an interval covers 3, 6, 7 or 9 distinct values at the most
significant digit, partition the range into 3 equi-width
intervals

If it covers 2, 4, or 8 distinct values at the most significant
digit, partition the range into 4 intervals

If it covers 1, 5, or 10 distinct values at the most
significant digit, partition the range into 5 intervals
Example of 3-4-5 Rule
count
Step 1:
Step 2:
-$351
-$159
Min
Low (i.e, 5%-tile)
msd=1,000
profit
Low=-$1,000
(-$1,000 - 0)
(-$400 - 0)
(-$200 -$100)
(-$100 0)
Max
High=$2,000
($1,000 - $2,000)
(0 -$ 1,000)
(-$4000 -$5,000)
Step 4:
(-$300 -$200)
High(i.e, 95%-0 tile)
$4,700
(-$1,000 - $2,000)
Step 3:
(-$400 -$300)
$1,838
($1,000 - $2, 000)
(0 - $1,000)
(0 $200)
($1,000 $1,200)
($200 $400)
($1,200 $1,400)
($1,400 $1,600)
($400 $600)
($600 $800)
($800 $1,000)
($1,600 ($1,800 $1,800)
$2,000)
($2,000 - $5, 000)
($2,000 $3,000)
($3,000 $4,000)
($4,000 $5,000)
Concept Hierarchy Generation for
Categorical Data




Specification of a partial ordering of attributes explicitly at the schema
level by users or experts
 street<city<state<country
Specification of a portion of a hierarchy by explicit data grouping
 {Urbana, Champaign, Chicago}<Illinois
Specification of a set of attributes.
 System automatically generates partial ordering by analysis of the
number of distinct values
 E.g., street < city <state < country
Specification of only a partial set of attributes
 E.g., only street < city, not others
Automatic Concept Hierarchy
Generation

Some concept hierarchies can be automatically generated
based on the analysis of the number of distinct values per
attribute in the given data set
 The attribute with the most distinct values is placed at
the lowest level of the hierarchy
 Note: Exception—weekday, month, quarter, year
country
15 distinct values
province_or_ state
65 distinct values
city
3567 distinct values
street
674,339 distinct values
VI. Summary

Data preparation is a big issue for both warehousing and
mining

Data preparation includes
 Data
cleaning and data integration
 Data
reduction and feature selection
 Discretization

A lot a methods have been developed but still an active area
of research
References
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E. Rahm and H. H. Do. Data Cleaning: Problems and Current Approaches. IEEE Bulletin of the
Technical Committee on Data Engineering. Vol.23, No.4
D. P. Ballou and G. K. Tayi. Enhancing data quality in data warehouse environments.
Communications of ACM, 42:73-78, 1999.
H.V. Jagadish et al., Special Issue on Data Reduction Techniques. Bulletin of the Technical
Committee on Data Engineering, 20(4), December 1997.
A. Maydanchik, Challenges of Efficient Data Cleansing (DM Review - Data Quality resource portal)
D. Pyle. Data Preparation for Data Mining. Morgan Kaufmann, 1999.
D. Quass. A Framework for research in Data Cleaning. (Draft 1999)
V. Raman and J. Hellerstein. Potters Wheel: An Interactive Framework for Data Cleaning and
Transformation, VLDB’2001.
T. Redman. Data Quality: Management and Technology. Bantam Books, New York, 1992.
Y. Wand and R. Wang. Anchoring data quality dimensions ontological foundations.
Communications of ACM, 39:86-95, 1996.
R. Wang, V. Storey, and C. Firth. A framework for analysis of data quality research. IEEE Trans.
Knowledge and Data Engineering, 7:623-640, 1995.
http://www.cs.ucla.edu/classes/spring01/cs240b/notes/data-integration1.pdf